[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 74 from proof refine-link (previous step)

cache_dirs[ino0] = mkdir(m4, md2, # links(ino0, cache_dirs), m10, entries), cache_dirs[ino1] = mkdir(m0, md3, # links(ino1, cache_dirs), m2, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries1[str]] = mkfile(m5, md1, # links(entries1[str], cache_dirs), content), cache_dirs[m9] = mkdir(m1, md4, # links(m9, cache_dirs), m13, entries2), entries0[str] = entries1[str], cache_files[entries1[str]] = mkfile(m3, md6, # links(entries1[str], cache_dirs), content1), entries[str] = entries1[str], cache_dirs[ino2] = mkdir(m7, md5, # links(ino2, cache_dirs), m11, entries1), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, mkinode(entries[str], md0, false, # links(entries[str], cache_dirs), 0, m6) = mkinode(m, md, boolvar, m8, m12, m14), afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), str ∈ entries0, ino1 ∈ cache_dirs, ino0 ∈ cache_dirs, str ∈ entries, ino2 ∈ cache_dirs, str ∈ entries1, m9 ∈ cache_dirs, entries1[str] ∈ cache_files, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m9, cache_dirs) ≠ ∅ ∨ m9 = ROOT_INO, links(ino1, cache_dirs) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino0, cache_dirs) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino2, cache_dirs) ≠ ∅ ∨ ino2 = ROOT_INO ⊦ ⟪icache_set# (mkinode (m9, cache_dirs[m9, mkdir(m1 + 1, md7, # links(m9, cache_dirs), m13, entries2[str0, entries1[str]])][m9].meta, true, cache_dirs[m9, mkdir(m1 + 1, md7, # links(m9, cache_dirs), m13, entries2[str0, entries1[str]])][m9].nlink, cache_dirs[m9, mkdir(m1 + 1, md7, # links(m9, cache_dirs), m13, entries2[str0, entries1[str]])][m9].nsubdirs, cache_dirs[m9, mkdir(m1 + 1, md7, # links(m9, cache_dirs), m13, entries2[str0, entries1[str]])][m9].size), false ; err, cache_icache); icache_set# (getinode (mkdentry(str, entries0[str]).ino, cache_dirs[m9, mkdir(m1 + 1, md7, # links(m9, cache_dirs), m13, entries2[str0, entries1[str]])], cache_files[entries1[str], mkfile(m3, md6, # links(entries1[str], cache_dirs) + 1, content1)] [entries[str], cache_files[entries1[str], mkfile(m3, md6, # links(entries1[str], cache_dirs) + 1, content1)] [entries[str], cache_files[entries1[str], mkfile(m3, md6, # links(entries1[str], cache_dirs) + 1, content1)][entries[str]].size:= m14 ] [entries[str] ] .meta:= md ]), false ; err, cache_icache); dcache_set#(m9, mkdentry(str0, mkdentry(str, entries0[str]).ino).name, mkdentry(str0, mkdentry(str, entries0[str]).ino); err, cache_dcache)⟫ ⟨old_dent0 := negdentry(str0); p_inode0 := mkinode(m9, md7, true, # links(m9, cache_dirs), m13, m1); p_inode1 := mkinode(entries0[str], md0, false, # links(entries[str], cache_dirs), 0, m6); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; cache_dirs3 := cache_dirs; cache_dirs4 := cache_dirs; afs_link#(mkdentry(str, entries0[str]); p_inode0, p_inode1, old_dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = cache_dirs3[m9, mkdir(m1 + 1, md7, # links(m9, cache_dirs3), m13, entries2[str0, entries1[str]])] ∧ afs_files = ( cache_files[entries1[str], mkfile(m3, md6, # links(entries1[str], cache_dirs2) + 1, content1)] [entries[str], mkfile(m6, md0, # links(entries1[str], cache_dirs2) + 1, content1) ] ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced0) ∧ (m9 ∈ cache_dirs3 ⊃ mkinode(m9, md7, true, # links(m9, cache_dirs3), m13, m1 + 1) ;mkinode (m9, (m9 = entries[str] ⊃ mkfile(m6, md0, # links(entries1[str], cache_dirs2) + 1, content1);cache_files[m9]).meta, false, (m9 = entries[str] ⊃ mkfile(m6, md0, # links(entries1[str], cache_dirs2) + 1, content1);cache_files[m9]).nlink, 0, (m9 = entries[str] ⊃ mkfile(m6, md0, # links(entries1[str], cache_dirs2) + 1, content1);cache_files[m9]).size) ) = p_inode0 ∧ (entries0[str] ∈ cache_dirs4 ⊃ mkinode (entries0[str], (entries0[str] = m9 ⊃ mkdir(m1 + 1, md7, # links(entries0[str], cache_dirs4), m13, entries2[str0, entries1[str]]) ;cache_dirs4[entries0[str]] ) .meta, true, (entries0[str] = m9 ⊃ mkdir(m1 + 1, md7, # links(entries0[str], cache_dirs4), m13, entries2[str0, entries1[str]]) ;cache_dirs4[entries0[str]] ) .nlink, (entries0[str] = m9 ⊃ mkdir(m1 + 1, md7, # links(entries0[str], cache_dirs4), m13, entries2[str0, entries1[str]]) ;cache_dirs4[entries0[str]] ) .nsubdirs, (entries0[str] = m9 ⊃ mkdir(m1 + 1, md7, # links(entries0[str], cache_dirs4), m13, entries2[str0, entries1[str]]) ;cache_dirs4[entries0[str]] ) .size) ;mkinode (entries0[str], (entries0[str] = entries[str] ⊃ mkfile(m6, md0, # links(entries1[str], cache_dirs4) + 1, content1) ;mkfile(m3, md6, # links(entries1[str], cache_dirs4) + 1, content1) ) .meta, false, (entries0[str] = entries[str] ⊃ mkfile(m6, md0, # links(entries1[str], cache_dirs4) + 1, content1) ;mkfile(m3, md6, # links(entries1[str], cache_dirs4) + 1, content1) ) .nlink, 0, (entries0[str] = entries[str] ⊃ mkfile(m6, md0, # links(entries1[str], cache_dirs4) + 1, content1) ;mkfile(m3, md6, # links(entries1[str], cache_dirs4) + 1, content1) ) .size) ) = p_inode1 ∧ mkdentry(str0, entries0[str]) = old_dent0 ∧ err = err0), str0 ∈ entries2

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 75:
cache_dirs[ino0] = mkdir(m4, md2, # links(ino0, cache_dirs), m10, entries), cache_dirs[ino1] = mkdir(m0, md3, # links(ino1, cache_dirs), m2, entries0), ((cache_files ⊕ cache_pcache) ⊕ cache_icache)[entries1[str]] = mkfile(m5, md1, # links(entries1[str], cache_dirs), content), cache_dirs[m9] = mkdir(m1, md4, # links(m9, cache_dirs), m13, entries2), entries0[str] = entries1[str], cache_files[entries1[str]] = mkfile(m3, md6, # links(entries1[str], cache_dirs), content1), entries[str] = entries1[str], cache_dirs[ino2] = mkdir(m7, md5, # links(ino2, cache_dirs), m11, entries1), afs_files = (cache_files ⊕ cache_pcache) ⊕ cache_icache, err = ESUCCESS, afs-cons(cache_dirs, cache_files), afs-cons(cache_dirs, (cache_files ⊕ cache_pcache) ⊕ cache_icache), dcache-cons(cache_dcache, cache_dirs, cache_files), icache-cons(cache_icache, cache_dirs, cache_files), pcache-cons(cache_pcache, cache_dirs, cache_files), synced(cache_dirs, cache_icache, cache_pcache), str ∈ entries0, ino1 ∈ cache_dirs, ino0 ∈ cache_dirs, str ∈ entries, ino2 ∈ cache_dirs, str ∈ entries1, m9 ∈ cache_dirs, entries1[str] ∈ cache_files, ¬ str0 ∈ entries2, cache_sync → synced(cache_files, cache_icache, cache_pcache), links(m9, cache_dirs) ≠ ∅ ∨ m9 = ROOT_INO, links(ino1, cache_dirs) ≠ ∅ ∨ ino1 = ROOT_INO, links(ino0, cache_dirs) ≠ ∅ ∨ ino0 = ROOT_INO, links(ino2, cache_dirs) ≠ ∅ ∨ ino2 = ROOT_INO ⊦ ⟪icache_set# (mkinode (m9, cache_dirs[m9, mkdir(m1 + 1, md7, # links(m9, cache_dirs), m13, entries2[str0, entries1[str]])][m9].meta, true, cache_dirs[m9, mkdir(m1 + 1, md7, # links(m9, cache_dirs), m13, entries2[str0, entries1[str]])][m9].nlink, cache_dirs[m9, mkdir(m1 + 1, md7, # links(m9, cache_dirs), m13, entries2[str0, entries1[str]])][m9].nsubdirs, cache_dirs[m9, mkdir(m1 + 1, md7, # links(m9, cache_dirs), m13, entries2[str0, entries1[str]])][m9].size), false ; err, cache_icache); icache_set# (getinode (mkdentry(str, entries0[str]).ino, cache_dirs[m9, mkdir(m1 + 1, md7, # links(m9, cache_dirs), m13, entries2[str0, entries1[str]])], cache_files[entries1[str], mkfile(m3, md6, # links(entries1[str], cache_dirs) + 1, content1)] [entries[str], cache_files[entries1[str], mkfile(m3, md6, # links(entries1[str], cache_dirs) + 1, content1)] [entries[str], cache_files[entries1[str], mkfile(m3, md6, # links(entries1[str], cache_dirs) + 1, content1)][entries[str]].size:= m14 ] [entries[str] ] .meta:= md ]), false ; err, cache_icache); dcache_set#(m9, mkdentry(str0, mkdentry(str, entries0[str]).ino).name, mkdentry(str0, mkdentry(str, entries0[str]).ino); err, cache_dcache)⟫ ⟨old_dent0 := negdentry(str0); p_inode0 := mkinode(m9, md7, true, # links(m9, cache_dirs), m13, m1); p_inode1 := mkinode(entries0[str], md, false, # links(entries[str], cache_dirs), 0, m14); cache_dirs0 := cache_dirs; cache_dirs1 := cache_dirs; cache_dirs2 := cache_dirs; cache_dirs3 := cache_dirs; cache_dirs4 := cache_dirs; afs_link#(mkdentry(str, entries0[str]); p_inode0, p_inode1, old_dent0, err0, cache_dirs, afs_files; afs_asynced)⟩ ( cache_dirs = cache_dirs3[m9, mkdir(m1 + 1, md7, # links(m9, cache_dirs3), m13, entries2[str0, entries1[str]])] ∧ afs_files = ( cache_files[entries1[str], mkfile(m3, md6, # links(entries1[str], cache_dirs2) + 1, content1)] [entries[str], mkfile(m14, md, # links(entries1[str], cache_dirs2) + 1, content1) ] ⊕ cache_pcache) ⊕ cache_icache ∧ (afs_asynced ↔ asynced0) ∧ (m9 ∈ cache_dirs3 ⊃ mkinode(m9, md7, true, # links(m9, cache_dirs3), m13, m1 + 1) ;mkinode (m9, (m9 = entries[str] ⊃ mkfile(m14, md, # links(entries1[str], cache_dirs2) + 1, content1);cache_files[m9]).meta, false, (m9 = entries[str] ⊃ mkfile(m14, md, # links(entries1[str], cache_dirs2) + 1, content1);cache_files[m9]).nlink, 0, (m9 = entries[str] ⊃ mkfile(m14, md, # links(entries1[str], cache_dirs2) + 1, content1);cache_files[m9]).size) ) = p_inode0 ∧ (entries0[str] ∈ cache_dirs4 ⊃ mkinode (entries0[str], (entries0[str] = m9 ⊃ mkdir(m1 + 1, md7, # links(entries0[str], cache_dirs4), m13, entries2[str0, entries1[str]]) ;cache_dirs4[entries0[str]] ) .meta, true, (entries0[str] = m9 ⊃ mkdir(m1 + 1, md7, # links(entries0[str], cache_dirs4), m13, entries2[str0, entries1[str]]) ;cache_dirs4[entries0[str]] ) .nlink, (entries0[str] = m9 ⊃ mkdir(m1 + 1, md7, # links(entries0[str], cache_dirs4), m13, entries2[str0, entries1[str]]) ;cache_dirs4[entries0[str]] ) .nsubdirs, (entries0[str] = m9 ⊃ mkdir(m1 + 1, md7, # links(entries0[str], cache_dirs4), m13, entries2[str0, entries1[str]]) ;cache_dirs4[entries0[str]] ) .size) ;mkinode (entries0[str], (entries0[str] = entries[str] ⊃ mkfile(m14, md, # links(entries1[str], cache_dirs4) + 1, content1) ;mkfile(m3, md6, # links(entries1[str], cache_dirs4) + 1, content1) ) .meta, false, (entries0[str] = entries[str] ⊃ mkfile(m14, md, # links(entries1[str], cache_dirs4) + 1, content1) ;mkfile(m3, md6, # links(entries1[str], cache_dirs4) + 1, content1) ) .nlink, 0, (entries0[str] = entries[str] ⊃ mkfile(m14, md, # links(entries1[str], cache_dirs4) + 1, content1) ;mkfile(m3, md6, # links(entries1[str], cache_dirs4) + 1, content1) ) .size) ) = p_inode1 ∧ mkdentry(str0, entries0[str]) = old_dent0 ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ mkinode(m, md, boolvar, m0, m1, m2) = mkinode(m3, md0, boolvar0, m4, m5, m6) ↔ m = m3 ∧ md = md0 ∧ (boolvar ↔ boolvar0) ∧ m0 = m4 ∧ m1 = m5 ∧ m2 = m6; (ws)